A tooth-positioning appliance for closing spaces has at least two appliance segments, each segment having a thin elastomeric shell with recesses for removably engaging a set of teeth, and tooth-clasping elements for removably engaging bonded attachments protruding from the teeth. One of the appliance segments includes a flat receptacle extending horizontally on the thin shell of the appliance segment, and the other appliance segment has a thin elongated tab extending laterally from the second appliance segment spanning the space to be closed, and in sliding engagement with the flat receptacle of the other appliance segment. An activating element is connected between the appliance segments to exert a force to change the size of the space between the sets of teeth as the tab slides with respect to the flat receptacle.
